Devising a Mathematical Formula for Time Travel

It took me a moment to get it, but when I did, I just knew that I had to work out a time-travel formula for East of Yesterday. I broke out my calculator, and got to work.

I mostly did this for fun. I didn’t expect it to be useful for the story.

I am not usually much of a math geek. I got as far as College Algebra, when I ambitiously took an accelerated class. I barely kept up. Matrices almost blew out my brain cells. College Algebra was my only C in college. After that, I barely clung to the Honor Roll. If I had taken the regular class, I might have moved on from there, but as it was, I was done. So I have never learned calculus. It’s right behind Latin on the list of things I want to learn before I die.

Anyway, I started with a real-life formula related to the one spoofed above:

Time = Distance / Speed

And I played with the numbers until I found a formula that worked for the travel times in my story. Here’s the formula for going back in time.

ThB = (ds)2

Time-hours Back equals distance times speed squared.

I suppose an example would be instructive.

distance = 100 miles
speed = 50mph

100 x 50 = 5000
5000 squared = 25,000,000 timehours

25,000,000 timehours divided by 8760 hours per year equals 2853.881 timedays
Divided by 356 days = 7.82 years traveled back.

I ignored leap years. This is fiction, after all. Here’s the formula to move forward.

ThF = π((ds)2)

Time-hours Forward equals pi times (distance times speed squared)

Why pi? Because what fun is a make-believe formula without it? Besides, I wanted travel to the future to be roughly three times “faster” than travel to the past, so I thought, why not pi? The only argument against it was because time is linear, not circular. But a character in my story had another opinion:

“So.” He clapped his hands together, obviously at a loss for what to say, “how was your trip?”

“Faster than I expected,” Adele said. “At least, the time-traveling part was. The rest of it was pretty awful.”

“Oh, yes—that.” He seemed relieved to be on a familiar subject. “It’s the added velocity of time that you experienced.”

“Added velocity?”

“Well, time moves forward, after all. So when you move forward in time, you have all that velocity behind you. When you go back, you have to work against that velocity. The multiplier is pi, to be precise, although I don’t know why that makes sense, since there is nothing circular about time.” He paused and then snapped his fingers. “Unless you’re traveling in time. Of course! Now it makes perfect sense.” He pulled a notebook out of his pocket and began to write.

(Please excuse the crudity of these paragraphs. I have not had a chance to edit or revise.)

Someone who has taken calc could perhaps critique my formulas. All I know is the numbers work for my story, and they let me know when the characters have moved too quickly (or slowly). And it made for some interesting revisions.